The present invention relates to a method for designing a sigma delta modulator (SDM). Furthermore, the present invention relates to a SDM having an enlarged maximum dynamic range compared to conventional SDM. Even further, the present invention relates to microphone modules, hearing aids, cellular phones and head-sets comprising a SDM according to the present invention.
SDMs have received much attention in recent years. The combination of over-sampling and noise shaping has revealed performance levels, which were not achievable just a years ago in integrated circuit technology. The principle can be used in many applications. Examples such as analog to digital converters, digital to analog converters, phase locked loops, PDM systems, PWM systems etc. have proven the versatility of this principle. The basic idea is that clock frequency is traded off for resolution.
A generic model (purely mathematical description) of a SDM shown in FIG. 1, consists of a pre-filter 101, a feedback filter 102 and a quantizer 103. The pre-filter and the feedback filter have the transfer-functions G(z) and H(z). To obtain a linear model of the modulator the quantizer is replaced by a linear gain block 104, and a noise source 105. The gain block has a gain of k. This model allows us to use all the standard mathematical tools available for linear systems for analysing the SDM.
To characterize the SDM two transfer functions are defined. These are the Signal Transfer Function (STF) and the Noise Transfer Function (NTF). The STF is defined as the transfer-function from the input of the modulator to the output. And the NTF is defined as the transfer-function from the quantization noise source to the output.
The two transfer functions are given by:       S    ⁢          xe2x80x83        ⁢    T    ⁢          xe2x80x83        ⁢          F      k        =                              k          ·                      G            ⁡                          (              z              )                                                1          +                      k            ·                          H              ⁡                              (                z                )                                                        ⁢              xe2x80x83            ⁢      N      ⁢              xe2x80x83            ⁢      T      ⁢              xe2x80x83            ⁢              F        k              =          1              1        +                  k          ·                      H            ⁡                          (              z              )                                          
Where k is the equivalent linear gain of a comparator.
A specific group of SDM, which are of special interest, is one bit single loop SDM. This type of SDMs have the advantage of being especially easy to implement in integrated circuit technology, and especially for low voltage applications the very simple implementation is advantageous.
One bit single loop SDMs comprise a plurality of integrators embedded in a feedback loop with a plurality of feedback branches. This topology forms the feedback filter 102 and the pre-filter 101. It can be shown that the NTF is a high pass filter function while the STF is a low pass filter-function. I.e. the quantization noise is suppressed at low frequencies while the low frequency input signal is passed unaffected through the modulator. A subsequent filter, digital or analog, can then remove the high frequency noise thus leaving the low frequency part of the signal with an improved signal to noise ratio.
When designing a SDM it is the design of the filter, which influences the performance of the SDM. It is of interest to choose the order and the coefficients of the filter in such a way that the noise is minimized in the frequency range of interest.
It is advantageous to design the NTF as a Butterworth filter as it has a low sensitivity to coefficient variations. A simplified Butterworth NTF is shown in FIG. 2. If the frequencies below the broken line 203 in the output of the SDM are the most important (such as in audio applications), then the NTF should suppress the lower frequency noise as much as possible. This can be achieved in two ways, either
1. by increasing the order of the filter and thereby increase the slope 205 of the noise transfer, or
2. by increasing the cut-off frequency 201.
For a filter of a given order, the only choice available is the choice of having a NTF with a very high cut-off frequency. However, there is an upper limit how much the cut-off frequency of the NTF can be increased. Increasing the cut-off frequency results in that the maximum stable amplitude (MSA) of the input signal decreases. All higher order SDM""s have the property that when the input signal""s amplitude exceeds a certain MSA value the SDM becomes unstable and starts to oscillate. The definition of a higher order SDM is that the number of integrators in the loop is larger than two.
To summarize, the trade-offs when choosing the cut-off frequency in the NTF are:
high cut-off frequency results in less noise and a lower MSA.
whereas
low cut-off frequency results in more noise and higher MSA.
According to the above, it is therefore of interest to design the filter in such a way that the optimal cut-off frequency is chosenxe2x80x94meaning a cut-off frequency resulting in maximum MSA vs. noise ratioxe2x80x94i.e. maximum signal to noise ratio (SNRmax). For each order of SDM""s and NTF filter function an optimum NTF cut-off frequency exists for which the SNRmax is maximized.
The modulator has to be capable of handling input signals larger than the MSA. A typical way of assuring stability of the modulator is to reset the integrators of the modulator when the amplitude of the input signal exceeds MSA. Instability can also be detected by monitoring the output signal, or it can be detected by monitoring, independently, the output signals of each integrator, and then resetting the integrators accordingly.
The above-mentioned way of accounting for instability is very effective, but unfortunately, it also introduces distortion in the output signal when the integrators are reset. An alternative way of ensuring stability is to limit the output swing of the integrators so that the signal swing at the output of each integrator do not increase uncontrollablexe2x80x94even in the situation when the input signal exceeds MSA causing the modulator to become unstable. This approach is very attractive as it introduces minimum distortion and gives a large dynamic range (DNR). Unfortunately, this approach is very difficult to implement in low voltage circuit design.
It is therefore of interest to establish a new and optimized design route for SDMs to ensure maximum DNR and stability while keeping the distortion in the output signal at a minimum for input signals exceeding MSA.
The dynamic range is defined as the ratio between the maximum output signal power and the output idle (no input signal) noise power.
When designing SDMs for use in low power/low voltage applications a variety of factors have to be taken into consideration since the implementation is not ideal compared to an ideal SDM. Examples of this being: non-infinite gain of integrators, circuit noise etc.
It is an object of the present invention to provide a new and optimized design route for SDMs for low power and low voltage applications to ensure maximum DNR, maximum SNRmax and maximum stability.
The above-mentioned object is complied with by providing, in a first aspect, a method for designing a sigma-delta-modulator comprising a plurality of cascaded integrators and a comparator, the method comprising the steps of:
providing an input signal to an input of the sigma-delta-modulator,
determining an amplitude of a signal at an output of at least one of the plurality of integrators,
adjusting the signal swing of the output signals of those of the integrators being placed closest in the signal path to the input of the sigma-delta-modulator by adjusting characteristics of those integrators in such a way that the signal swing of those integrators being placed closest to the input is significantly smaller than the signal swing of the remaining integrators.
By cascaded integrators is meant that an integrator output is connected to the input of a following integrator. An integrator can in an embodiment be realized using digital or analog electronics.
A comparator is a component transforming the amplitude continuous input signal to an amplitude discrete output signal having either a first or a second value. The input of the SDM may be the input of the first integrator in the cascade of integrators.
Typically, the output signals are determined for all integrators even though only some of them are affected in terms of having their outputs reduced. The adjusting of the characteristics of the integrators may be done by adjusting the gain of the integrators and/or values of feedback factors.
The adjusting step may be performed by
adjusting the signal swing of the output signal of a first integrator to a first value, and
adjusting the signal swing of the output signal of a second integrator to a second value, the second value being larger than the first value.
The integrators being placed closest in the signal path to the input of the sigma-delta-modulator may be the two integrators being placed immediately after the input. The signal swing of the output signal of these two integrators may be below 20 percent of the full scale output signal level of the quantizer. The signal swing of the remaining integrators are adjusted so as to increase along the signal path.
Again, the adjusting step may be performed by adjusting gain parameters of the integrators, such as adjusting the feedback gain.
In a second aspect, the present invention relates to a sigma-delta-modulator comprising a plurality of cascaded integrators and at least one comparator, the sigma-delta-modulator being designed using a method according to the first aspect of the present invention.
In a third aspect, the present invention relates to a method of controlling a sigma-delta-modulator comprising a plurality of cascaded integrators and a comparator, the method comprising the steps of:
monitoring the signal swing of an output signal of at least one of the plurality of integrators and determining if the monitored signal swing exceeds a predefined threshold value, and
in case the monitored signal swing exceeds the predefined threshold value reducing the output signal with a predefined factor or value so as to bring the monitored signal swing below the predefined threshold value.
Thus, if the signal swing at the output of the integrators should become close to unstable (the predefined threshold value) the reduction with the predefined factor or value ensures that instability never occurs and the integrators"" signal swing remains stable.
The predefined threshold value may be associated with a maximum stable input amplitude of the sigma-delta-modulator.
The input signal being introduced may be within the range of 95-99% of a predefined MSA. The signal swings at the output of the integrators is reduced resulting in very low sensitivity to circuit imperfections.
In a fourth aspect, the present invention relates to a sigma-delta-modulator comprising a plurality of cascaded integrators, at least one comparator, and means for performing a method according to the third aspect of the present invention.
In a fifth aspect, the present invention relates to a sigma-delta-modulator having a maximum signal (S) to noise (N) plus total harmonic distortion (THD) ratio, S/(N+THD), being larger than a predetermined value, said predetermined value being determined from a maximum stable amplitude value and a noise power value, the maximum stable amplitude value and the noise power value being derivable from an obtainable noise transfer function associated with the sigma-delta-modulator.
The predetermined value may be determined using the expression   20  ⁢      xe2x80x83    ⁢      log    10    ⁢            MSA      rms              Noise      rms      
wherein MSArms is a root mean square value of the maximum stable amplitude value, and wherein Noiserms is the root mean square value of the noise power value which may be derived by summing the energy of the idle noise in the band of interest.
MSArms may be derived from the Gaussian ability criterion by solving the equation:       Min    ⁡          (              A        ⁡                  (          K          )                    )        =            1      -              M        ⁢                  xe2x80x83                ⁢        S        ⁢                  xe2x80x83                ⁢                  A          peak          2                            1      -              M        ⁢                  xe2x80x83                ⁢        S        ⁢                  xe2x80x83                ⁢                  A          peak          2                    -                        2          π                ⁢                  e                                    -              2                        ·                                          (                                                      erf                                          -                      1                                                        ⁡                                      (                                          MSA                      peak                                        )                                                  )                            2                                          
where A (K)=2-norm(NTF(K))xe2x80x94i.e. the two-norm of the impulse of NTF as a function of the quantizer gain K.
If the signal is a sine wave then MSArms=MSApeak/sqrt(2).
The sigma-delta-modulator may comprise a plurality of integrators and a least one comparator. The plurality of integrators may be cascaded.
In a sixth aspect, the present invention relates to a microphone module comprising a sigma-delta-modulator according to the second or to the fifth aspect of the present invention. This microphone module may form part of a hearing aid, a cellular phone, or a head-set.
In a seventh aspect, the present invention relates to a mobile unit comprising a sigma-delta-modulator according to the second or to the fifth aspect of the present invention. The mobile unit may be selected from the group consisting of hearing aids, cellular phones, or head-sets.